To add categories to your main menu. Go to Appearance > Menus. In the bottom left menu, the Image Categories should be listed. You might have to click View All to see them all. Click the box of the category you want to add and click Add to Menu. You will see a bar with your Image Category show in the main window. Drag that where you want it appear in the Main Menu. If you want a child category, like Animals > Birds, drag the Birds category under the parent category until it is indented, then release. Be sure to click Save Menu before you leave the page. (it will ask you as a reminder, thank goodness. I have forgotten to save many times!)
Also, if Image Categories don't show in the left menu, go to the top right bar and click Screen Options. Make sure Categories is checked there.